Problem: Two masses are placed on two frictionless inclines as shown. Determine the acceleration and tension in the connecting cord.

Solution:  I draw the free bodies with the same orientations they have in the diagram:

Sometimes you can tell which way the acceleration is. There's no doubt in this case, and I have chosen the positive direction that way in both diagrams. Suppose you couldn't tell? Then you would choose an arbitrary direction as positive in one free body, and a consistent direction for the other free body. For example, if I had chosen down & to the left for the left free body, I should choose up and to the left for the other. (The value of a would then come out negative, indicating that the original direction was wrong. Try it!!)

Writing the equations and substituting...

Adding the equations (so T subtracts out), I get:

Equations for the y-directions were unnecessary because the normal forces were not involved. This will change when we consider friction.